COD-121 unified session list: welcome list frontend (slice A, unit 2)

Backs the welcome-screen "Resume Conversation" list with the new
GET /api/sessions/unified endpoint instead of /api/history/sessions, so it
shows the COMPLETE set (live + persisted + non-Claude + closed history)
newest-first with richer context, rather than only Claude transcripts.

- terminal-ui.js: new _fetchUnifiedSessions(); loadHistorySessions() now uses
  it. _buildHistoryItem upgraded to the unified shape (kept backward-compatible
  with the folder-modal's old shape): title = name || firstPrompt || dir; a
  mode badge + a LIVE badge (sources includes 'live'); timestamp from
  lastActivityAt (falls back to lastModified); size only when present; detail
  panel + "View all in this folder" preserved (gated on projectKey). Resume
  branches: an open live session selects its tab, a closed one resumes.
- unified-session-service.ts + endpoint: pass projectKey through the history
  source so the folder drill-down survives.
- styles.css: .history-item-badges / -badge / -badge-live pills.

Verified: tsc 0, lint 0, frontend-syntax + public-asset format clean, service
tests 13/13 (+projectKey), route tests 4/4. Playwright on an isolated beta:
the welcome list renders real items from /api/sessions/unified, and the
renderer produces the tab-name title + codex mode badge + visible LIVE badge,
omits LIVE on closed items, keeps "View all in folder", and routes resume
correctly (open->select tab, closed->resume). Persistent panel + live SSE
status are later units.

src/web/public/styles.css

@@ -2822,6 +2822,32 @@ body.touch-device .terminal-container .xterm .xterm-helper-textarea {
   font-weight: 500;
 }
 
+/* Badge row (mode + LIVE pills) sits between the title and subtitle (COD-121). */
+.history-item-badges {
+  display: inline-flex;
+  flex-wrap: wrap;
+  gap: 0.3rem;
+  align-items: center;
+}
+
+.history-item-badge {
+  font-size: 0.55rem;
+  font-weight: 600;
+  text-transform: uppercase;
+  letter-spacing: 0.03em;
+  line-height: 1;
+  padding: 0.12rem 0.35rem;
+  border-radius: 0.35rem;
+  background: var(--bg-hover);
+  color: var(--text-muted);
+  white-space: nowrap;
+}
+
+.history-item-badge-live {
+  background: color-mix(in srgb, var(--green) 22%, transparent);
+  color: var(--green);
+}
+
 .history-item-meta {
   font-size: 0.7rem;
   color: var(--text-muted);